I'm going into my first psychiatric job here in the UK and I've been offered an HCA place at a Cygnet CAMHS unit and a place at an NHS trust. The pay at the Cygnet job is about 3500 pounds a year more which is these low paid positions can make a difference to survival. The CQC reports on both places are much of a muchness in terms of provision of services. The Trust does seem more innovative in coming up with new methods of patient care, having psychologists and OTs on the wards 7 days a week.

Will getting experience in private sector be just as valid in trying for my next role or in trying for an assistant psychologist position?

Whether your HCA position is for a private company or the NHS is unlikely to matter. All else being equal, I would choose whichever role interests you the most. Of course, with £3500 salary difference, they are definitely not equal.